Sid (the sloth) and Diego (the sabre-tooth tiger) decide to have a competition to see who is the fastest! They will both race down a snowy hill - the first animal to reach the bottom of the hill wins! The competition will continue until either Diego or Sid has won two races. The probability of Sid winning a race is 0.4. After that, Sid's probability of winning a race is 0.7 if he has won the previous race, but only 0.2 if he has lost the previous race. a) Copy and complete the tree diagram on your own paper, and show all the probabilities of the possible outcomes of the competition. Pr(Outcomes) Sid Wins Race Sid Wins Sid Wins Race Race Diego Wins Race Diego Wins Race Sid Wins Race Diego Wins Sid Wins Race Race Diego Wins Race Diego Wins Race b) Find the probability that: i) Sid will win the competition i) Diego will win the competition c) Who is more likely to win the competition? Why?P... Question 4 continued... d) Let X be the number of races run until the competition is complete. i) Is X a binomial random variable? Explain why or why not. i) Find the probability distribution of X. X 2 3 Pr (X = x) iii) Find the expected number of races that the competition will take, E(X) iv) Find the variance of the number of races that the competition will take, correct to 4 decimal places. e) Given that the competition lasted three races, find the probability that Diego won